Question

find the pair of integers whose product is the first integer and whose sum is the second integer -40,-6

Answer 1

`x;y-the\ integers\\\\ \left\{\begin{array}{ccc}xy=-40&(1)\\x+y=-6&\to x=-6-y&(2)\end{array}\right\\\\subtitute\ (2)\ to\ (1):\\\\(-6-y)(y)=-40\\(-6)(y)+(-y)(y)=-40\\-6y-y^2=-40\\-y^2-6y+40=0\ \ \ \ |change\ the\ signs\\y^2+6y-40=0\\y^2+10y-4y-40=0\\y(y+10)-4(y+10)=0\\(y+10)(y-4)=0\iff y+10=0\ or\ y-4=0\\\boxed{y=-10\ or\ y=4}`


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